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A006248 Number of primitive sorting networks on n elements. Number of projective pseudo order types: simple arrangements of pseudo-lines.
(Formerly M3428)
1, 1, 1, 1, 1, 4, 11, 135, 4382, 312356, 41848591, 10320613331 (list; graph; refs; listen; history; text; internal format)



J. Bokowski, personal communication.

J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 102.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=1..12.

J. Bokowski & N. J. A. Sloane, Emails, June 1994

S. Felsner and J. E. Goodman, Pseudoline Arrangements. In: Toth, O'Rourke, Goodman (eds.) Handbook of Discrete and Computational Geometry, 3rd edn. CRC Press, 2018.

J. Ferté, V. Pilaud and M. Pocchiola, On the number of simple arrangements of five double pseudolines, arXiv:1009.1575 [cs.CG], 2010; Discrete Comput. Geom. 45 (2011), 279-302.

Lukas Finschi, A Graph Theoretical Approach for Reconstruction and Generation of Oriented Matroids, A dissertation submitted to the Swiss Federal Institute of Technology, Zurich for the degree of Doctor of Mathematics, 2001.

L. Finschi, Homepage of Oriented Matroids

L. Finschi and K. Fukuda, Complete combinatorial generation of small point set configurations and hyperplane arrangements, pp. 97-100 in Abstracts 13th Canadian Conference on Computational Geometry (CCCG '01), Waterloo, Aug. 13-15, 2001.

Fukuda, Komei; Miyata, Hiroyuki; Moriyama, Sonoko. Complete Enumeration of Small Realizable Oriented Matroids, arXiv:1204.0645 [math.CO], 2012; Discrete Comput. Geom. 49 (2013), no. 2, 359--381. MR3017917. - From N. J. A. Sloane, Feb 16 2013

D. E. Knuth, Axioms and Hulls, Lect. Notes Comp. Sci., Vol. 606, Springer-Verlag, Berlin, Heidelberg, 1992.

Index entries for sequences related to sorting


Asymptotics: a(n) = 2^(Theta(n^2)). This is Bachmann-Landau notation, that is, there are constants n_0, c, and d, such that for every n>=n_0 the inequality 2^{c n^2} <= a(n) <= 2^{d n^2} is fulfilled. For more information see e.g. the Handbook of Discrete and Computational Geometry. - Manfred Scheucher, Sep 12 2019


Cf. A006245, A006246, A018242, A063666. A diagonal of A063851.

Sequence in context: A167418 A055979 A018242 * A119571 A089920 A303881

Adjacent sequences:  A006245 A006246 A006247 * A006249 A006250 A006251




N. J. A. Sloane


a(11) from Franz Aurenhammer (auren(AT)igi.tu-graz.ac.at), Feb 05 2002

a(12) from Manfred Scheucher and Günter Rote, Sep 07 2019



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Last modified February 24 21:55 EST 2021. Contains 341592 sequences. (Running on oeis4.)